Question

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.

Answer 1

Let O be the centre of the circle with radius 5.6 cm and OACB be its sector with perimeter 27.2 cm.
Thus, we have:
$$\begin{gathered} OA+OB+arcAB=27.2 \\ \Rightarrow 5.6+5.6+arcAB=27.2 \\ \Rightarrow arcAB=16\mathrm{cm} \end{gathered}$$
Now,
Area of the sector OACBO$=\left(\frac{1}{2}\times \mathrm{Radius}\times l\right)\mathrm{square}\mathrm{units}$
$$\begin{gathered} =\left(\frac{1}{2}5.6\times 16\right){\mathrm{cm}}^2 \\ =44.8{\mathrm{cm}}^2 \end{gathered}$$